math

A square whose side is 2m has it's corner cut away so as to form a octagon with all sides equal find the length of each side of octagon and also find the area of the octagon?

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  1. if the cutout of each side is x, the side of the octagon is x√2.

    Also, 2x + x√2 = 2, so
    x = 2-√2
    the octagon side s = 2(√2-1)
    check: 2(2-√2) + 2(√2-1) = 2

    area of octagon with side s = 2s^2 (1+√2)
    so, for us, that is 2(1+√2)(2√2-2)^2 = 8(√2-1)

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